Question

If

A + B = E
B - A = C
A + D = Q
D - B = L

then

A + C - B = ?

Answer 1

From the second equation, A + C = B
So A + C - B = B - B = 0
Other equations are unwanted.

Answer 2

Since B - A = C,
therefore 0 = C - B + A
Or A + C - B = 0

Answer 3

A + B = E ......... (1)
B - A = C .......... (2)
A - D = Q ........... (3)
D - B = L ............. (4)

taking eqn (1) - eqn (2) gives ;
2A + C = E ................. (5)

then eqn (3 ) - eqn (4) gives ;
A + B = Q - L ............... (6)

last taking eqn (5) - eqn (6) gives ;
A + C - B = E + L - Q ; which is the required equation

So;
A + C - B = E + L - Q

Answer 4

A + B = E
- B + A = -C Second equation multiplied by -1
-A - D = -Q
D - B = L
By adding the four equations, we obtain : A - B = E - C - Q + L
Then A + C - B = E - Q + L